A company observed that its revenue has increased by 
 every year from 
 to 
. If the revenue of the company in the year 
 was 
, which equation represents the yearly revenue (
) of the company 
 years after 
?
Responses

R = x ( 0.9 ) t

R = x ( 1.1 ) t

R = x + 0.9 t

R = x + 1.1 x t



To determine the correct equation for the yearly revenue $ R $ of the company $ t $ years after a specific year, we need to consider how the revenue changes over time.

Given that the revenue increases by a certain percentage every year, this suggests an exponential growth model. The general form of an exponential growth equation is:

\[
R = x \cdot (1 + r)^t
\]

where:
- $ x $ is the initial revenue,
- $ r $ is the rate of increase (expressed as a decimal),
- $ t $ is the number of years after the initial year.

Given the options:

1. $ R = x \cdot (0.9)^t $ suggests a decrease by 10% every year (not applicable here since revenue is increasing).
2. $ R = x \cdot (1.1)^t $ suggests an increase by 10% every year (this is likely the correct option).
3. $ R = x + 0.9t $ suggests a linear increase, not exponential.
4. $ R = x + 1.1 \times t $ also suggests a linear increase, not exponential.

Given the information provided, the correct equation representing the yearly revenue $ R $ is:

\[
R = x \cdot (1.1)^t
\]

This represents a 10% increase in revenue each year.

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Would you like further details or have any questions? 

Here are 5 related questions for further exploration:

1. How do you calculate the compound annual growth rate (CAGR) from revenue data over several years?
2. How does the exponential growth formula change if the revenue increased by a different percentage?
3. What would the revenue be after 5 years if the initial revenue $ x $ was $100,000?
4. How does the choice between linear and exponential models affect revenue predictions?
5. What real-world factors might cause a company's revenue growth to deviate from this model?

**Tip:** Exponential growth models are commonly used for financial forecasting because they accurately represent consistent percentage increases over time.

A company observed that its revenue has increased by 10% every year from a specific year. If the revenue of the company in the year X was Y, which equation represents the yearly revenue (R) of the company t years after X? Possible options are: R = x (0.9)^t, R = x (1.1)^t, R = x + 0.9t, or R = x + 1.1 * t.

Explore how to model a company's revenue growth with a 10% annual increase using the exponential growth formula R = x * (1.1)^t. This problem helps understand exponential functions in real-world financial contexts and is suitable for students in Grades 9-12.

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